Properties

Label 16.6.a
Level 16
Weight 6
Character orbit a
Rep. character \(\chi_{16}(1,\cdot)\)
Character field \(\Q\)
Dimension 2
Newform subspaces 2
Sturm bound 12
Trace bound 3

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Defining parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 6 \)
Character orbit: \([\chi]\) = 16.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(12\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(16))\).

Total New Old
Modular forms 13 3 10
Cusp forms 7 2 5
Eisenstein series 6 1 5

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)Dim.
\(+\)\(1\)
\(-\)\(1\)

Trace form

\( 2q - 8q^{3} - 20q^{5} + 112q^{7} + 58q^{9} + O(q^{10}) \) \( 2q - 8q^{3} - 20q^{5} + 112q^{7} + 58q^{9} - 664q^{11} + 60q^{13} + 2128q^{15} - 604q^{17} - 3880q^{19} + 576q^{21} + 3920q^{23} + 2142q^{25} - 2384q^{27} - 3876q^{29} + 1472q^{31} - 4000q^{33} + 2976q^{35} + 10028q^{37} - 14576q^{39} + 8340q^{41} + 21288q^{43} - 16964q^{45} - 22368q^{47} - 25294q^{49} + 31088q^{51} + 31180q^{53} - 19984q^{55} + 50848q^{57} - 9208q^{59} - 53220q^{61} - 4944q^{63} - 57944q^{65} - 6280q^{67} + 52928q^{69} + 78832q^{71} + 62676q^{73} - 49528q^{75} - 50496q^{77} + 32352q^{79} - 97742q^{81} - 135080q^{83} + 120728q^{85} + 58512q^{87} + 101748q^{89} - 25312q^{91} - 165632q^{93} + 180112q^{95} - 73532q^{97} + 33992q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(16))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2
16.6.a.a \(1\) \(2.566\) \(\Q\) None \(0\) \(-20\) \(-74\) \(24\) \(+\) \(q-20q^{3}-74q^{5}+24q^{7}+157q^{9}+\cdots\)
16.6.a.b \(1\) \(2.566\) \(\Q\) None \(0\) \(12\) \(54\) \(88\) \(-\) \(q+12q^{3}+54q^{5}+88q^{7}-99q^{9}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(16))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(16)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ 1
$3$ (\( 1 + 20 T + 243 T^{2} \))(\( 1 - 12 T + 243 T^{2} \))
$5$ (\( 1 + 74 T + 3125 T^{2} \))(\( 1 - 54 T + 3125 T^{2} \))
$7$ (\( 1 - 24 T + 16807 T^{2} \))(\( 1 - 88 T + 16807 T^{2} \))
$11$ (\( 1 + 124 T + 161051 T^{2} \))(\( 1 + 540 T + 161051 T^{2} \))
$13$ (\( 1 - 478 T + 371293 T^{2} \))(\( 1 + 418 T + 371293 T^{2} \))
$17$ (\( 1 + 1198 T + 1419857 T^{2} \))(\( 1 - 594 T + 1419857 T^{2} \))
$19$ (\( 1 + 3044 T + 2476099 T^{2} \))(\( 1 + 836 T + 2476099 T^{2} \))
$23$ (\( 1 + 184 T + 6436343 T^{2} \))(\( 1 - 4104 T + 6436343 T^{2} \))
$29$ (\( 1 + 3282 T + 20511149 T^{2} \))(\( 1 + 594 T + 20511149 T^{2} \))
$31$ (\( 1 - 5728 T + 28629151 T^{2} \))(\( 1 + 4256 T + 28629151 T^{2} \))
$37$ (\( 1 - 10326 T + 69343957 T^{2} \))(\( 1 + 298 T + 69343957 T^{2} \))
$41$ (\( 1 + 8886 T + 115856201 T^{2} \))(\( 1 - 17226 T + 115856201 T^{2} \))
$43$ (\( 1 - 9188 T + 147008443 T^{2} \))(\( 1 - 12100 T + 147008443 T^{2} \))
$47$ (\( 1 + 23664 T + 229345007 T^{2} \))(\( 1 - 1296 T + 229345007 T^{2} \))
$53$ (\( 1 - 11686 T + 418195493 T^{2} \))(\( 1 - 19494 T + 418195493 T^{2} \))
$59$ (\( 1 + 16876 T + 714924299 T^{2} \))(\( 1 - 7668 T + 714924299 T^{2} \))
$61$ (\( 1 + 18482 T + 844596301 T^{2} \))(\( 1 + 34738 T + 844596301 T^{2} \))
$67$ (\( 1 - 15532 T + 1350125107 T^{2} \))(\( 1 + 21812 T + 1350125107 T^{2} \))
$71$ (\( 1 - 31960 T + 1804229351 T^{2} \))(\( 1 - 46872 T + 1804229351 T^{2} \))
$73$ (\( 1 + 4886 T + 2073071593 T^{2} \))(\( 1 - 67562 T + 2073071593 T^{2} \))
$79$ (\( 1 + 44560 T + 3077056399 T^{2} \))(\( 1 - 76912 T + 3077056399 T^{2} \))
$83$ (\( 1 + 67364 T + 3939040643 T^{2} \))(\( 1 + 67716 T + 3939040643 T^{2} \))
$89$ (\( 1 - 71994 T + 5584059449 T^{2} \))(\( 1 - 29754 T + 5584059449 T^{2} \))
$97$ (\( 1 - 48866 T + 8587340257 T^{2} \))(\( 1 + 122398 T + 8587340257 T^{2} \))
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